WRT a circulation pump, in a pressurized, closed system, the head pressure isn't much of an issue...the water falling back down helps pull the water up from the WH. The pump only needs to overcome friction and open the checkvalve. Read the spec sheet carefully on the tankless system, it may not allow a recirculation pump (voids the warranty), or if it does, may require other items as well.
Rather than use a timer, some of them can be fitted with a momentary activation circuit...in this, when you want hot water, you press a button, and the recirculation system runs until you have hot. At least you wouldn't be dumping water down the drain, but you would have to wait the same amount of time for the pump to bring hot to the tap.
Your problem is not unique to a tankless system...you'd have the same issue with a tank. The tankless may be slightly longer, since it does have some ramp-up time to actually generate some hot verses a tank where you are only flushing the lines with already hot water.
Having lived with tankless systems in both Europe and in the USA, I must say that I still prefer a tank, especially if you have a boiler to heat it. Tankless does work well when it can be close to the point of use, and is sized adequately for the local incoming water temp and the anticipated max use.